Doesn't really matter how many QT players you have, they're just players. You can also have Flip, VLC, WFM, and a dozen others. The codecs are not necessarily part of the players' installer payloads but you don't need QTv7. There's something likely to be broken in the ProRes codecs. I gotta say, though, that's highly unlikely. They're just codecs, pretty benign. But if the code for the OS resource is damaged at all, the app trying use it won't succeed.

Windows or MacOS? There was a recent update to the Pro video resources so you can check the App Store for updates. Latest is 2.0.4 and included changes to the ProRes family. You can force that update to reload by going into your Library/receipts folder and deleting the item for this update.

I don't know anything about PCs, sorry.

Your uploaded image appears on my browser as a period in tiny black box.

If Premiere freezes when trying to encode into ProRes, than you've likely got a bigger issue on your hands than just an AE problem. Something has gone awry with your system. Have any third-party codec packs every been installed on that machine? Has any external previewing hardware been installed like Blackmagic, Kona, Matrox, AJA?